Transcript Direct Variation

Main Idea and New Vocabulary
Example 1: Find a Constant Ratio
Key Concept: Direct Variation
Example 2: Solve a Direct Variation
Example 3: Identify Direct Variation
Example 4: Identify Direct Variation
Key Concept: Linear Functions
• Use direct variation to solve problems.
• direct variation
• constant of variation
Find a Constant Ratio
FINANCIAL LITERACY The amount of money
Serena earns at her job is shown on the graph.
Determine the amount Serena earns per hour.
Find a Constant Ratio
Since the graph of the data forms a line, the rate of
change is constant. Use the graph to find the
constant ratio.
Answer: Serena earns $10 per hour.
SHOPPING The cost of softballs is shown on the
graph. Determine the cost per softball.
A. $0.27 per softball
B. $3.75 per softball
C. $6.00 per softball
D. $12.00 per softball
Solve a Direct Variation
SHOPPING The total cost for cans of soup varies
directly as the number of cans purchased. If 4 cans
of soup cost $5, how much would it cost to buy
8 cans?
Write an equation of direct variation. Let x represent
the number of cans and let y represent the total cost.
y = kx
Direct variation
5 = k(4)
y = 5, x = 4
1.25 = k
Simplify.
y = 1.25x
Replace k with 1.25.
Solve a Direct Variation
Use the equation to find y when x = 8.
y = 1.25x
Write the equation.
y = 1.25(8)
x=8
y = 10
Multiply.
Answer: So, it would cost $10 to buy 8 cans.
SHOPPING The total cost for sports drinks
varies directly as the number of bottles
purchased. If 6 bottles cost $7.50, how much
would it cost to buy 9 bottles?
A. $7.20
B. $10.00
C. $11.25
D. $15.00
Identify Direct Variation
Determine whether the linear function is a direct
variation. If so, state the constant of variation.
Compare the
ratios to check
for a common
ratio.
Answer: The ratios are not the same. The function is
not a direct variation.
Determine whether the linear function is a direct
variation. If so, state the constant of variation.
A. Yes; the constant of
variation is 54.
B. Yes; the constant of
variation is –54.
C. No; the ratios are not
proportional.
D. No; the ratios are not
greater than 1.
Identify Direct Variation
Determine whether the linear function is a direct
variation. If so, state the constant of variation.
Identify Direct Variation
Answer: Since the ratios are the same, the function
is a direct variation. The constant of variation
is
or 8.5.
Determine whether the linear function is a direct
variation. If so, state the constant of variation.
A. Yes; the constant of variation is –32.5.
B. Yes; the constant of variation is 32.5.
C. No; the ratios are not proportional.
D. No; the ratios are not greater than 1.